5. Find the equation of the line passing through the point P = (-3 , 3)
     and perpendicular to the graph of 3y = 6x + 3 .
      a. y = 2x + 3     b. y = -(1/2)x + 3/2     c. y = -(1/2)x - 3/2     d. y = 2x - 3

 6. The domain of the function defined by the equation   is
      a.    b.    c.  d.

 7.  The domain of  the function defined by the equation   is
    a.    b.   c.   d. 

 8. Perform the indicated matrix operation, if possible: 
    a.      b.      c.      d. 

 9. At a cafeteria one "lunch" consists of one sandwich,one bag of chips, and one drink.
     There are four types of sandwich: roast beef , turkey, bologna, and ham.
     There are five different drinks and three different kinds of chips.
     How many different "lunches" are available?
   a. 120     b. 60    c. 24    d. 21    e. 12
 10. Determine the inverse function of 

    a.      b.      c. d. 

 11. On a roll of one die, what is the probability of obtaining an even number or a 3?
    a. 1/3     b. 2/9     c. 2/3     d.  1/9

12. In how many ways can a committee of 5 people be chosen from a group of 7 people?
    a. 2,520     b. 42     c. 1,260     d. 21

13. Let x, y, and z be positive numbers. Write this expression as the logarithm of a single quantity:
      2 log₄ x + 3 log₄ y - 3 log₄ z
    a.      b.      c.      d. 

14. Solve     log 4x + log x = 2     for x.        a. 5     b. 4     c. 3     d. 2

15. Assume that f(x) = x + 3 and g(x) = x² - 1. Then (g o f) (x) = x² + 6x + 8.    a. true    b. false

16. Solve for x:   | 3x - 5 | = 10   List all solutions for x.    a. 5     b. 5/3     c. 5, -5/3     d. -5, 3

17.  Assume that f(x) = x + 3 and g(x) = x² - 1. Then ( f - g )(x) =  -x² + x + 4.   a. true    b. false

18.  Assume that f(x) = x + 3 and g(x) = x² - 1. Then (g + f )(2) =    a. 2    b. 4    c. 6     d. 8

19. Determine the inverse function of 2y = 3x + 5.
    a.        b.     c.    d. 

20. Find the equation of the line passing through point P( 0 , 4 )
        and parallel to the graph of     3y = 6x + 3.
    a. y = 3x + 6      b. y = 2x + 4     c. y = 4x + 2     d. y = 6x + 3

21. Solve     log (2x + 3) = log (4x - 9)     for x.
    a. 6     b. 3.58     c. 0.78     d. 4

22. Consider the points   P(3, -3)   and Q(-3,5).   Find the distance between P and Q.
    a. 2     b. 8     c. 11     d. 10

23. Draw one card from a well-shuffled standard deck of 52 cards.
        What is the probablilty of drawing a red card or an ace?
    a.   22/52     b . 24/52    c. 26/52    d. 28/52   e. 30/52
24. Write the solution set of this inequality in interval notation. 
    a.      b.      c.      d. 

25. Assume that f(x) = x² + 3 and g(x) = x - 1. Find ( g f )(3).    a. 11     b. 14     c. 24     d. 10

26. Farmer Pat is going to plant corn and soybeans on 400 acres. If Pat plants 200 more acres of corn than soybeans, how many acres of corn does Pat plant?
    a. 100    b. 133    c. 150    d. 200    e. 300
27. Perform the indicated matrix operation, if possible. 
     a.    b.   c.   d.

28. Write the solution set of the inequality  in interval notation.
    a. [-4, 1]     b.    c.    d. (-1, 4)

29. Find the inverse of the matrix  , if possible. If no inverse exists, so indicate.
    a.     b.    c.  No inverse    d.

30.   Calculate the value of $1,000 left on deposit for 10 years at an annual rate of 8% ,
        compounded quarterly. Ignore pennies. Recall that
                                                                                    
    a. $2,208     b. $2,193     c. $4,321     d. $3,095

31. Consider the points P (5,7) and Q (-3,-7). Find the midpoint of segment PQ.
    a. (4,7)     b. (1,0)     c. (4,0)     d. (1,7)

32. Solve the following system of equations for all variables. Use any method.
      x + y +  z = 4
    2x - y + 3z = 5
      x + 2y - z = 0         The y and z coordinates of the solution are:
    a. y = -2; z = 3     b. y = 2; z = 3     c. y = 3; z = 4     d. y = 3; z = 2

33. Solve the following system of equations for all variables. Use any method.
        3x  - 2y = -7            The x-coordinate of the solution is:
       -2x + 3y = 3                  a. -2     b. 3     c. -3     d. 2

34. Solve 3^{(x - 1)} = 2 for x.    a. 2.73     b. 1.63     c. 2.58     d. -0.18

35. For log₄64 = x, find the value of x.    The answer is 3.    a. true    b. false

36. Find the equation of the line passing through points P(5,4) and Q(-6,-4)
    a. y = -(8/11)x - 4     b. y = (8/11)x + 4     c. y = (8/11)x + 4/11
    d. y = (8/11)x - 4/11

37. Write the solution set of    in interval notation.
    a.     b. [-6,6]     c.     d. 

38. Find the vertex of the parabola whose equation is 2x² + 8x - y + 20 = 0.
    a. (-2,3)     b. (3,-2)     c. (-2,12)     d. (-3,2)

39. The solution set of the inequality x² -3x + 4 < 2  is
    a. (2,4)     b. (1,2)    c. (-2, -1)    d. (4,2)

40. The solution set of  is
    a.        b.       c.     d. 

41. Solve 4 = 5^x for x.        a. 0.86     b. 0.1     c. 1.16     d. -0.1

42. Solve the following system of inequalities by using the graphing method.
        y ≤ x + 3
        y ≥ 1 - 2x             The solution:
    a. contains the point (2,-3)        b. is totally in QI & QIV
    c. contains the origin    d. is totally in QII & QIII

43. Given the slope m =  2/3   and the y-intercept  b = - 4  , find the equation of the line.
    a. y = (3/2)x - 4    b. y = (2/3)x - 4    c. y = (-3/2)x + 4     d. y = - (2/3)x + 4

44. Perform the indicated matrix operation, if possible. 
    a.     b.     c.     d.

45. For the set of ordered pairs  { (1,1) , (2,3) , (1,2) } which one of the following is true?
    a. It is neither a function nor a relation.        c. It is not a function, but it is a relation.
    b. It is a function, but it is not a relation.      d. It is both a function and a relation.

46. Is the relation   a function?         a. yes    b. no

47. Write in exponential form: log₅25 = 2.     The answer is 5² = 25.     a. true    b. false

48. Write in logarithmic form:   4^-2 = 1/16    The answer is  log₄ (1/16)  = -2.   a. true    b. false

49. Let matrix  ; find the inverse of A.
     The element at the position second row, first column of  A^-1  is
        a. -0.25     b. -0.5     c. 0     d. 0.875

50. 
    a.     b.     c.     d. 

51. Let  ; find .    a. -5    b. -3     c. 3    d. 7

The following table represents annual number of days of unhealthy air in Los Angeles as a function of  year.

x	1988	1989	1990	1991	1992	1993
f (x)	226	212	163	157	169	131

52.  Find .
    a. 212     b. 186     c. 157    d. 169

53. Refer to the table in problem #52. What was the average rate of change (in days per year) from 1988 to 1993?
    a. 5    b. 19    c. -19    d. 95

54. Compute the average rate of change of  from x = 0.5 to x = 4.5.
    a. 91.125    b. -0.875    c. 4    d. 20.75

55. Solve for  x: 
    a.{ x | x = 3 or x = 2 }    b.{ x | x = -3 or x = 2 }     c.{ x | x = 3 or x = -2 }    d.{ x | x = -3 or x = -2 }

56. Solve for x:   Recall that for    ,  .
    a.     b.     c.     d. 

57. Solve :  ;    x   is approximately
    a. 2.264    b. 2.274    c. 2.284    d. 2.294

58. Let  ,  then 

    a. 0.5     b. 1    c. 1.5    d. 2
 

59.  S = {(1, 2), (2,3), (4,5), (1,3)}. Is S a function?   a) yes   b) no

60.  S = { (-3, 7), (-1, 7), (3, 9), (6, 7), (10, 1)}. Is S a function?   a) yes   b) no

61.  S is given by the following table. Is S a function?

a) yes   b) no

62.  Which of the following best describes the function f(x) = -2x + 5?

a) f is a linear function    b) f is a nonlinear function   c) f is a constant function   d) f is a constant, linear function

63.  Determine if the data in the table is linear or nonlinear. If the data is linear, state the slope of the line passing through the data points.

a) linear, slope of 3/2     b) linear, slope of 3/4     c) linear, slope of 6/5     d) nonlinear

64.  Let f(x) = 4x² – 2x + 2. Find f(k – 3).

a) f(k – 3) = 4k² – 2k – 4     b) f(k – 3) = 4k² – 2k + 44     c) f(k – 3) = 4k² – 26k + 44     

d) f(k – 3) = 4k² – 26k + 32

Use the scenario to answer questions 65 - 68:  

A 500 gallon tank initially contains 200 gallons of fuel oil. A pump is filling the tank at a rate of 6 gallons per minute.

65.  Which of the following formulas for a linear function f models the number of gallons of fuel oil in the tank after x minutes?

a)   f(x) = 6x + 500       b)   f(x) = 500x + 6     c)   f(x) = 200x + 500    d)   f(x) = 6x + 200

66.  Which of the following represents the graph of f?

a)                                                 b)                                                       c)                                 

d)

67.  What is an appropriate domain for f?

a) D = {0 £ x £ 500}       b) D = {0 £ x £ 200}      c) D = {0 £ x £ 50}        d) D = {200 £ x £ 500}

68. Which of the following is the y-intercept?

a) y = 6    b) y = 50     c) y = 200      d) y = 500

Use the following scenario to answer questions 69 - 70.

In 1990, the number of births per 1000 people in the United States was 16.7 and decreasing at 0.326 births per 1000 people each year.

69. Which of the following is the formula for a linear function f that models the birth date in year x, where x = 0 corresponds to 1990, x = 1 to 1991, and so on?

a) f(x) = 16.7 - 0.326x     b) f(x) = 16,700 – 326x   c) f(x) = 16.7 + 0.326x     d) f(x) = 16,700 + 326x

70. Which of the following is an estimation of the birth rate in 1997?

a) 18, 982    b) 14.418      c) 18.982     d) 14,418

71.  The following graph models average tuition and fees in dollars at public 4-year colleges from 1981 to 1995. Which of the following is the point-slope form of the line?

a) y = 132(x – 1984) + 1225      b) y = –132(x – 1984) – 1225     c) y = 0.0076(x – 1984) + 1225      d) y = -0.0076(x – 1984) – 1225

72.  Solve the linear equation  with the intersection-of-graphs method. Which of the following is an approximation of the solution to the nearest thousandth?

a)   -2.262      b)   -0.800      c)  23.673      d)   2.262

73.  Solve the linear equation   with the intersection-of-graphs method. Which of the following is an approximation of the solution to the nearest thousandth?

a)    -29.429     b)   -147.143     c)   -6.727    d)  -2.405

Use the following function for problems 74 - 76.

Given f(x) = 2x + 1 if -3 £ x < 0

                   x - 1 if 0 £ x £ 3

a) D = { -3 £ x £ 3}   b) D = { -3 £ x < 3} c) D = { -3 < x £ 3} d) D = { -3 < x < 3}

75.  Evaluate f(-2), f(0), and f(3).

a) f(-2) = -3; f(0) = -1; f(3) = 2      b) f(-2) = 3; f(0) = -1; f(3) = 7

c) f(-2) = 3; f(0) = -1; f(3) = 2       d) f(-2) = -3; f(0) = 1; f(3) = 7

76.  Which of the following represents the graph of f?

a)                                                    b)                                                     c)

d)

Use the table to evaluate each expression, if possible, for problems 77 - 80.

77.  (f + g)(2) =         a) 5      b) 7      c) -2       d) undefined

78.  (f - g)(4) =          a) 15     b) 5     c) 10      d) undefined

79.  (f g)(-2) =           a) 0       b) 6      c) 5       d) undefined

80.  (f /g)(0) =           a) 0       b) 6      c) 5       d) undefined

For problems 81 - 84, use the graph to evaluate each expression.

81.  (f + g)(0) =         a) 2      b) 0      c) 3      d) 1

82.  (f - g)(-1) =        a) -2     b) 0      c) -3      d) 1

83.  (f g)(1) =            a) 0       b) 1      c) 2      d) 3

84.  (f /g)(2) =          a) -2      b) 4      c) -1/2  d) 1/2

85.  Given f(x) = 1-x and g(x) = 3x+1. Identify the domain for (fg)(x).

a) (-¥ , ¥ )     b) (-¥ , -4)     c) (-4, ¥ )     d) (-¥ , -4) È (4, ¥ )

86.  Given f(x) = 2x and g(x) = 3-4x. Identify the domain of (f +g)(x).

a) (-¥ , ¥ )     b) (-¥ , -4)     c) (-4, ¥ )     d) (-¥ , -4) È (4, ¥ )

87.  At an intersection, cars arrive randomly with an average rate of 50 cars per hour. The likelihood or probability that at least one car will enter the intersection within a period of x minutes can be estimated by f(x) = 1 - e^(-5x/6). Find the likelihood that at least one car enters the intersection during a 3 minute period.

a) .918      b) .997       c) .429      d) 0.82

88.  Expand: log 6/z

a) log 6 + log z       b) log 6 - log z       c) log z - log 6      d) log z + log - 6

89.  Expand log 2x⁷/3k

a) log 2x + log 3k       b) 7 log x + log 2 - log 3 + log k       c) 7 log x + log 2 - log3 - log k 

d) 7 log x + 7 log 2 - log 3 - log k

90.  How long does it take for $1000 to double in value if the interest rate is 8.5% compounded quarterly?  Hint:  
                

a) 8.24 years      b) 33 years       c) 7.8 years      d) 16.5 years

91.  Solve the following absolute value equation: |4x-5| = 5

a) {0, 5/2}   b) {1, 3/2}   c) {1}   d) no solution

92.  Solve the following inequality: |T - 43| £ 24

a) (-¥ , 19] È [67, ¥ )       b) [24, ¥ )       c) [19, 67]      d) (-¥ , 24]

93.  The total balances that were outstanding on a revolving credit totaled $500 billion in 1996 and $560 billion in 1998. Using the midpoint formula, estimate the debt in 1997.

a) 15 billion   b) 530 billion   c) 1248.5 billion   d) 60 billion

The table below lists the actual annual cost y to drive a midsize car 15,000 miles per year for selected years x.

94.  Find the least squares regression line that models this data:

a) y = 145.45 x -284,341.2       b) y = .006667715x + 1955.530819     c) y = .977999857 x - 280361.2      

 d) y = 143.45x + 280361.2

95.  A homeowner has 80 feet of fence to enclose a rectangular garden. What dimensions for the garden give the maximum area?

a) 80 feet x 80 feet      b) 20 feet x 40 feet       c) 20 feet x 20 feet       d) 40 feet x 40 feet

96.  The graph of f(x) = ax² + bx + c is given below. Use it to solve ax² + bx + c = 0.

a) {-2, 6}      b) {-6, 2}      c) {-3, 1}      d) {-5}

97.  Water is leaking out of a hole in the bottom of a 100 gallon tank. The table below lists the volume of water in the tank V, after t minutes.

Which function models the data best?

a) f(t) = 0.4t² -9.9t + 100     b) g(t) = 100 - 9.5t

98.  Admission prices to a movie are $4 for children and $7 for adults. If 75 tickets were sold for $456, how many of each type of ticket were sold?

a) 61 child, 14 adult      b) 23 child, 47 adult      c) 23 child, 52 adult      d) 52 child, 23 adult

99.  A music store has compact discs that sell for three prices, marked A, B, and C. The last column in the table shows the total cost of a purchase. Use this information to determine the cost of one CD of each type by setting up a matrix and solving it with an inverse.

a) Type A: $10.99; Type B: $12.99; Type C: $14.99

b) Type A: $14.99; Type B: $12.99; Type C: $10.99

c) Type A: $17.27; Type B: $12.59; Type C: $13.32

d) Type A: $11.99; Type B: $12.99; Type C: $14.99

100.  In how many arrangements can 3 students from a class of 15 give a speech?

a) 455      b) 2730       c) 3375       d) 5

101.  Suppose 8 people enter an event in a swim meet. In how many ways could the gold, silver, and bronze medals be awarded?

a) 3       b) 336       c) 56       d) 24

102.  On a test involving 6 essay questions, students are asked to answer 4 questions. How many ways can the essay questions be selected?

a) 360      b) 6       c) 15       d) 4

103.  In 1999, a total of 100404 new books and editions were published. The table lists the number of books published in specific areas. If a new book or edition is selected at random, find the probability that its subject area is art or music.

a) 0.054      b) 0.54       c) 0.031      d) 0.00049

104. Find an equation that shifts the graph of f by the indicated amounts: